Watch balance

ABSTRACT

A WATCH BALANCE COMPRISING AT LEAST TWO INERTIA-BLOCKS HAVING A STREAMLINED SHAPED CARRIIED BY ARMS AND EXTENDING ON THE WHOLE OVER LESS THAN THE HALF OF THE CIRCUMFERENCE OF THE BALANCE, THE REST OF THE CIRCUMFERENCE BEING FREE OF MATERIAL, CHARACTERIZED IN THAT THE COMPACTNESS OF THE INERTIA-BLOCKS IN THE RANGE OF FROM .310 TO .455 AND THE MATERIAL COMPRISING THE INERTIA-BLOCKS A DENSITY EXCEEDING 9 G./CM.3.

Dec. 14, 1971 F. BoNsAcK 3,626,691

WATCH LANCE Filed Aug. 25, 1969 2 sheets-sheet 1 Flll 6 y l ,7, ya, 1 ,y32, l @A INVENTOR.

fRANcois oNsAcK l Dec. `QQ'T u A F, BONSASK' 3,626,69

WATCH BALANCE Filed Aug. 25, 1969 2 Sheets-Sheet 2 INVENTOR. FRANCOISBONSACK ATTORNEYS United States Patent Office 3,626,691 WATCH BALANCEFrancois Bonsack, Le Locle, Switzerland, assignor to Les FabriquesdAssortiments Reunies, Le Locle, Neuchatel, Switzerland Filed Aug. 25,1969, Ser. No. 852,559 Claims priority, application Switzerland, Sept.6, 1968, 13,444/ 68 Int. Cl. G04b 1 7/ 00 U.S. Cl. 58-107 6 ClaimsABSTRACT F THE DISCLOSURE A watch balance comprising at least twoinertia-blocks having a streamlined shape carried by arms and extendingon the Whole over less than the half of the circumference of thebalance, the rest of the circumference being free of material,characterized in that the compactness of the inertia-blocks in the rangeof from .310i to .4155 and the material comprising the inertia-blocks adensity exceeding 9 g./cm.3.

The present invention relates to a watch balance.

The energy consumed by a balance-hairspring assembly increases with theamplitude and, roughly, also with the moment of inertia. This is awell-known relation, and if an engineer notes that on a caliber theamplitude of the oscillation is too small, either he will endeavor toincrease the force of the main spring, or else he will choose a smallerbalance, having a smaller moment of inertia, which, for the sameavailable energy, will oscillate with a larger amplitude.

0n the contrary, if it is desired to increase the per formances withrespect to the stability and the precision of a Watch, the moment ofinertia of the balance is increased as far as possible, whereby thefactor of quality Q of the oscillator can be increased. It is known thatQl=1rN, wherein N=number of the periods of a damped,`

non-sustained oscillator in orderthatits amplitude falls to 1/ e of itsinitial value, e being the basis of the natural logarithms, Forinstance, on the marine chronometers, balances having a high moment ofinertia are used, and these balances necessitate, therefore, in orderthat their oscillations can be sustained, a considerable power.

In a watch, especially for a small caliber (ladys watch) the availableenergy is limited. If it is sought to increase the moment of inertia andthe factor of quality, one isl rapidly stopped by the amplitude whichbecomes too small. 'I'his limitation has become particularly sensiblewith the present trend to increase the frequency of oscillation, for thepurpose of increasing the factor of quality. Now, an oscillator of highfrequency consumes more energy, and the engineer is induced to diminishthe moment of inertia of the balance in order to keep a sufficientamplitude, so that the increase of the factor of -quality is not asimportant as expected.

'In short, the technical problem to be solved is the following:

How is it possible to minimize the consumption of energy of a balancehaving a given moment of inertia? A's a matter of fact, any reduction ofthe consumption of energy for a given moment of inertia will enable theengineer to choose, for a given available power and a given frequency,balances of larger moment of inertia, and this will enhance orfavor thefactor of quality Q.

How is it possible to reduce the energy lost upon the oscillation of abalance? It is at first important to know where the energy is going, bywhich physical processes it is dissipated. These losses are due:

3,626,691 Patented Dec. 14, 1971 (a) to the friction of the balanceagainst air; (b) to the friction of the pivots; (c) to the internalfriction of the hairspring.

The present invention aims at reducing the factor (a), i.e. the frictionof the balance against air,

In the balances of conventional shape, which are uncut and have acircular rim, this friction is only lateral (for the rim), since thelatter always occupies the same portion of space when the balanceoscillates. A front resistance (resistance to the penetration) onlyoccurs for the edges of the balance arms. It is reasonable to think thatthis friction will be proportional to the rim area and that it will alsodepend on the peripheral speed (which is itself proportional to theradius, for a given angular velocity). This explains Why the balanceshaving a high moment of inertia consume more energy; in order toincrease the moment of inertia, it is necessary to increase either themass (and this will, for a constant density, increase the rim area), orthe radius and this will increase the peripheral speed). Other factorsintervene, but the energy portion dissipated by friction against airroughly increases with the moment of inertia.

The engineer is, therefore, induced to think that an increase of thedensity of the material used 'will be favorable, since, for a givenmass, the rubbing surface will diminish. On the other hand, there existsa radical method for eliminating the friction of air, and this consistsin causing the balance to oscillate in the vacuum.

However, another diiculty is encountered. 'Ihe friction of air has astabilizing effect on the amplitude of the balance spring torque whenthe spirng uncoils), The balances made of a very dense material oroscillating in the vacuu-m consume little energy, but their amplitudeconsiderably diminishes between the moment when the mainspring iscompletely wound up and after 24 hours, and this iinds expression invariations of the daily rate if only the period varies with theamplitude (lack of isochonism).

The engineer seeks, therefore, to obtain an oscillator the consumptionof which is as low as possible, but which does not show a too large fallof amplitude when the available power diminishes by a given percentage.

The engineer is thus induced to study the curve giving the consumedpower in function of the amplitude. The inventor has shown (in JournalSuisse dHorlogerie, Swiss edition, No. 9/10, 1967, pages 339-345) thatif the total friction torque F in function of the angular velocity 0 isgiven by the consumed power P in function of the amplitude fp is P= awp%bw2 p2 Cco3go3 w=21rv. v=frequency of the oscillation.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a graph depicting dissipatedpower P as a function of amplitude rp for an oscillating system of thetype treated by the invention;

FIG. 2 is a graph depicting the derivative dP/dq; as a function of (pwhere P and p are the same parameters as in IFIG. l;

FIG. 3 is a top View of an embodiment of the invention;

FIG. 4 is a cross-sectional view taken along line 4-4 of FIG. 3;

FIGS. 5, 6 and 7 are, respectively, plan views of further embodiments ofthe invention.

DETAILED DESCRIPTION OF THE INVENTION The curve giving P in function ofthe amplitude p has the aspect shown in FIG. l of the accompanyingdrawing. In this ligure, the letters have the following meanings:

Pozavailable power when the mainspring is wound up p=correspondingamplitude P24=available power after working during 24 hoursp24=corresponding amplitude A=difference of amplitude It will be seenimmediately that the difference of amplitude A, will depend on theaverage slope of the curve in the domain of utilization; the larger isthis slope, the smaller will be 13,. This slope is given by:

The problem, therefore, amounts to reducing P0 while keeping asuflicient slope between p0 and w24. But P0 is connected with the slope:

If the curve of the derivative dP/dq in function of p is represented,the curve Z shown in FIG. 2 of the accompanying drawing is obtained. Inthis representation, P0 will be the area of the surface situated belowthe curve Z up to the abscissa ipo. The problem, therefore, amounts todiminishing the surface lying below the curve Z, While keeping theordinate at the point of abscissa (p0,

The ordinate dP/d at the point of abscissa (p0 may be divided into threesegments:

In the same manner, the surface P0 may be divided into three portions:

The quantities Pa, Pb and Pc are connected in a simple manner with Pa',Pb and Pc:

It is desired to keep P (00) =Pa{-Pb\-Pc constant. It is, therefore,only possible to carry out transfers between the Pa', Pb and Pc (forinstance subtract a certain quantity AP from Pa and distribute it overPb and Pc).

Since the purpose is to diminish the surface lying below the curve Z,i.e. P0' it will immediately be seen in which manner these transfershave to be effected: For instance, the term -Pa has to be reduced (whichhas to be multiplied by p0 in order to obtain the corresponding surfaceportion) and the terms Pb and Pc have to be increased (these terms haveto be multiplied only by 00/ 2 and po/3, respectively, in order toobtain the corresponding surfaces).

a=socalled dry coeflicient of friction, proportional to the weight ofthe balance and to the radius of the pivot;

b=socalled viscous coeicient of friction, proportional (as concerns thepart due to the friction of air on the rim), to S and to Rmz;

c=socalled quadratic coefficient of friction, proportional to S and toRm3.

There exists, therefore, a simple method for increasing Pb and Pc' atthe expense of Pa' Without reducing the moment of inertia: Rm has to beincreased, and this permits (for the same moment of inertia) reducingthe mass (moment of inertia- #mRnF), and therefore Pa'. Since Pb and Pcare proportional to km2 and to Rm3, respectively, they will increasewith the radius and the engineer will obtain what he desires, viz areduction of P0 without changing P at p0. The diminution of the massresults, I admit, for the same density and radius, in a diminution ofthe rim area, but since the radius is increased while reducing the mass,a slimmer rim, having a larger circumference, and therefore lesscompact, is obtained, so that the diminution of the mass does notproduce a diminution of the area.

It is also sought to diminish the masses lying near the center andwhich, therefore, do not contribute to increase the moment of inertianor to stabilize the amplitude: masses of the balance staff, of theroller and also of the arms. This permits reducing Pa' and accordi-nglyincreasing Pb and/or Pc.

The increase of the radius will also permit favoring Pc at the expenseof Pb', since Pc is proportional to Rm3, whereas Pb is proportional toRm2.

Summarizing, a reduction of the mass with an increase of the radiuspermits diminishing Pa' at the expense of Pb' and Pc; in addition, itpermits increasing Pc' more than Pb', but it does not permit diminishingPb. Now, a diminution of Pb' at the expense of Pc would permit furtherreducing Po without altering P ((po).

In order to reduce b, it is necessary to diminish the rim area withoutdiminishing its moment of inertia.

A first method is to increase the density of the material used for therim. Thus, the rim area is reduced, so that Pb and Pc are diminished;then, the radius has to be increased in order to restore P p0); since Pcincreases more quickly with the radius than Pb', it is possible toobtain all things considered a diminution of Pb at the expense of Pc.

But, here too, there is a limitation: Since the volume` of the rimdiminishes and the radius increases, the engineer is led to very littlecompact shapes wherein the area becomes important with respect to thevolume, so that an optimal radius is quickly attained, beyond which theconsumption due to Pb and Pc becomes too important. The obstacle is,therefore, the little compactness; if this obstacle is to be overcome,it is necessary to try to use more compact shapes.

The engineer is, therefore, induced to wonder whether it would not beadvantageous to abandon the conti-nuous rim and to distribute the massof inertia into separate portions, this introducing, I admit, frontfrictions (which may again be reduced by using stream-lined shapes), butpermitting obtaining a larger compactness and, therefore, a smaller areafor a given volume. The calculation and the experience have confirmedthis supposition: The introduction of a front friction is largelycompensated by the diminution of the side friction consecutive to thediminution of the area. And this is precisely the subject-matter of thepresent invention. The invention proposes a balance having separatemasses, preferably presenting a stream-lined profile, carried lby arms.For reasons of equilibrium, at least two symmetrical masses arerequired. The engineer is even induced Definition of the Compactness Thefollowing quantity is defined as a measure for the Compactness:

y= xi/If/x/"S or, if several bodies are present, or, if several bodiesare present,

wherein V=volume of the body, S=area of the body.

This measure offers the advantage that it depends only upon the shape,and not upon the size (y is invariant if al1 of the linear dimensions ofa body are multiplied by the same factor).

EXAMPLES Compactness of a sphere (maximum Compactness) Compactness of acube Overall Compactness of two spheres of the same radius Compactnessof an ordinary continuous rim of rectangular cross-section h=height ofthe rim s=width of the rim The compactnesses of the rim of the ordinarybalances (dimensions according to the norms of the Swiss watch industry)are about .248-.264.

The present invention relates to a watch balance, consisting of at leasttwo inertia-blocks or weights carried by arms and extending on the wholeover less than the half of the circumference of the balance, the rest ofthe circumference being free of material, this balance beingcharacterized in that the Compactness of the inertiablocks is greaterthan .310, and is preferably greater than .320. The Compactness referredto as the Compactness of the mass of inertia alone (inertia-blocks andpossible balancing screws), the arms adapted to sustain this mass ofinertia not included. If the inertia-blocks are pieces .manufacturedseparately from the arms, the arm portion situated outside the innerradius of the inertia-block is considered as belonging to the mass ofinertia.

The balance illustrated in FIGS. 3 and 4 includes two identicalinteria-blocks or weights 1 and 2 carriedv by arms 3 and 4,respectively. Each of the inertia-blocks presents two pyramid-shapedends 5, in order to reduce the front frictions on the oscillation of thebalance. The width of the arms 3 and 4 is fairly larger than theirthickness. Both inertia-blocks 1 and 2 extend on the whole over lessthan the half of the circumference of the balance, the rest of thecircumference being free of material. In the example illustrated, theCompactness of the inertia-blocks is about .35. The density of theinertiablocks 1 and 2 is preferably rather large; it may for instanceexceed 9 g./cm.3. The number of the inertiablocks might be greater thantwo and may include three or more arms 3a, 4a and 6, carrying weights1a, 2a and 7 respectively, as shown in FIG. 7. The pyramids 5, in whichend the inertia-blocks may be more or less blunt or paraboloidal 5',FIG. 5, and might also be replaced by half-spheres 5", FIG. 6.

1. A watch balance, consisting of at least two inertiablocks carried byarms and extending on the whole over less than the half of thecircumference of the balance, the rest of the circumference being freeof material, characterized in that the Compactness of the inertia-blocksis in the range of from .310 to .455, the material comprising saidblocks having a density exceeding 9 g./cm.3, and said inertia-blockshaving a streamlined shape which converges symmetrically toward theopposite ends thereof,

whereby to establish streamline flow past said block and reduce thefront friction during oscillation of the balance.

2. A watch balance according to claim 1, characterized in that theinertia-blocks are in the number of two.

3. A watch balance according to claim 1, characterized in that theinertia-blocks are in the number of three.

4. A watch balance according to claim 1, wherein said ends are ofgenerally pyramidic shape and converge to points.

5. A watch balance according to claim 1, wherein said ends are ofgenerally paraboloidal shape.

6. A watch balance according to claim 1, wherein said ends arehalf-spheres.

References Cited UNITED STATES PATENTS FOREIGN PATENTS 4/1969 Fnance58-107 9/1959 Switzerland 58- 107 RICHARD B. WILKINSON, Primary ExaminerS. A. WAL, Assistant Examiner

